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Understanding Digital Circuits and Signals: Noise Margins, Logic Conversion, and Binary Operations

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Learn about noise margins, logic circuits, binary conversion, BCD, hexadecimal representation, and binary addition. Understand two’s complement, binary numbers, and subtraction.

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Understanding Digital Circuits and Signals: Noise Margins, Logic Conversion, and Binary Operations

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  1. Digital Circuits

  2. Analog and Digital Signals

  3. VM Noise margins in Logic Circuits

  4. VDD "1" V OH Noise margin high NM H V IH Undefined Region V NM Noise margin low L IL V OL "0" VGND Gate Input Gate Output Noise margins in Logic Circuits

  5. Digital to Binary Conversion Conversion of the integer part

  6. Digital to Binary Conversion Conversion of the fractional part

  7. A B A B A B A B 0 0 1 1 2 2 3 3 C C C C C i ,0 o ,0 o ,1 o ,2 o ,3 FA FA FA FA = ( C ) i ,1 S S S S 0 1 2 3 Binary Addition A B C One bit binary adder Sum Carry

  8. Binary Coded Decimal and Hexadecimal Representation To get BCD replace each digit by a group of 4 bits 3786.1=0011 0111 1000 0110. 0001BCD Binary to hexadecimal conversion (0,1,..9,A,..,F) 1110 1010 1001 0101=EA9516 Exercise: Represent 25 by its BCD and binary codes

  9. Binary Coded Decimal and Hexadecimal Representation To get BCD replace each digit by a group of 4 bits 3786.1=0011 0111 1000 0110. 0001BCD Binary to hexadecimal conversion (0,1,..9,A,..,F) 1110 1010 1001 0101=EA9516 Exercise: Represent 25 by its BCD and binary codes 25/2 = 12 rem 1 12/2 = 6 rem 0 6/2 = 3 rem 0 3/2 = 1 rem 1 1/2 = 0 rem 1 25 = 0010 0101BCD 25 = 0001 1001

  10. Binary and Grey Codes

  11. Binary and Grey Codes

  12. Two’s Complement and Binary Addition One’s complement id obtained by inverting all the bits Two’s complement is obtained as one’s complement + 1 invert

  13. Positive and Negative Binary Numbers Signed two’s complement of a number is used a the negative number value. This can be used in subtraction operation.

  14. Positive and Negative Binary Numbers This can be used in subtraction operation. To subtract number B from A we add two’s complement of B to A • Example: Compute A-B=25-11 using binary adders • Find binary representations A= , B= • Find two’s complement of B -B= • Add A+(-B) using binary notation

  15. Positive and Negative Binary Numbers This can be used in subtraction operation. To subtract number B from A we add two’s complement of B to A • Example: Compute A-B=25-11 using binary adders • Find binary representations A=011001, B=001011 • Find two’s complement of B -B=110101 • Add A+(-B) using binary notation • 011001 • +110101 • 001110 = 14

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